Physical Transport Using the Technique of Explicit Differences

1 Physical Transport Using the Technique of Explicit Differences 

Here the new concentration in a cell with the coordinates x and y at the time (t-i-At) is calculated from its own concentration at the precedent time t and the concentrations of its four neighbours, also at time t. In this calculation the following constants will be considered The size of a cell in Ax and Ay direction, the length of a time step At, the two dispersion coefficients Di in direction of flow and Dv vertical, as well as the linear groimdwater velocity Vg. 

The explicit difference method has the disadvantage of a tendency to oscillation, in case the time steps are too large. On the other hand it is relatively simple to handle and can be programmed straight forward, because it requires only a direct assignment per cell according to the equation above. For this study we decided to choose the explicit difference method, since it was possible to avoid oscillations due to rather moderate time steps (Courant criterion). 

The cells at the edge of the modelled flow field require special handling. In our example, where we modelled a vertical profile through the aquifer, these are the cells at the front, back, top and bottom of the flow field. 

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